Architecture and Hyper-parameters: 
CaFi-Net predicts a 128 dimensional invariant embedding for each point in space and performs convolution at resolutions \(1/2\) , \(1/4\) , and \(1/8\) . Each equivariant convolution layer aggregates features from  512 neighboring points at twice the resolution. We then use equivariant non-linearities introduced in [1]} by applying Batch Normalization [2]} and ReLU activation [3]} in the inverse spherical harmonic transform domain. We use a three layer MLP to with intermediate Batch Normalization and ReLU layers followed by a final linear layer to predict canonical coordinates. To train our network, we weigh the canonicalization loss (\(\mathcal {L}_{canon}\) ) the highest with weight \(2.0\)  and \(1.0\)  for all the other loss functions.
All our models are written in PyTorch [4]} and are trained for 300 epochs with batch size of 2 on an Nvidia 1080-Ti GPU. We use the Adam Optimizer [5]} with initial learning rate of \(6e-4\)  and L2 weight regularization of \(1e-5\)  for all our experiments.
Please see the supplementary document for more details.
